How do I make my walking animation to continuously move instead of stopping at the end of the frame
You can do that by changing how the interpolation is in the Graph editor.

1.Open up the graph editor and make sure you're on F-Curves;

2.Select all necessary keyframes and press Shift + E;

3.Now a little menu will appear, click on "Make Cyclic (F Modifier).

There, now your animation should be what you want.